Results 31 to 40 of about 65 (63)
, 2003 Compact K hler solvmanifolds are classified up to biholomorphism. A proof of a conjecture Benson and Gordon, that completely solvable compact K hler solvmanifolds are tori is deduced from this. The main ingredient in the proof is a restriction theorem for polycyclic K hler groups proved by Nori and the author.
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Maximal symmetry and unimodular solvmanifolds [PDF]
Pacific Journal of Mathematics, 2019 Recently, it was shown that Einstein solvmanifolds have maximal symmetry in the sense that their isometry groups contain the isometry groups of any other left-invariant metric on the given Lie group. Such a solvable Lie group is necessarily non-unimodular.
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Symplectic Bott–Chern cohomology of solvmanifolds [PDF]
Journal of Symplectic Geometry, 2019 (Table 3 has been corrected.)
ANGELLA, DANIELE, Kasuya, Hisashi
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Examples of Compact Lefschetz Solvmanifolds
Tokyo Journal of Mathematics, 2002 A symplectic manifold \((M^{2m},\omega)\) is called a Lefschetz manifold if the mapping \(\wedge\omega^{m-1}: H^1_{DR}\to H^{2m-1}_{DR}\) on \(M\) is an isomorphism. By a solvmanifold is meant a homogeneous space \(G/\Gamma\) where \(G\) is a simply connected solvable Lie group and \(\Gamma\) is a lattice.
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The Anosov theorem for exponential solvmanifolds [PDF]
Pacific Journal of Mathematics, 1995 The authors exhibit a class \({\mathcal N} {\mathcal R}\) of compact solvmanifolds such that for any \(S \in {\mathcal N} {\mathcal R}\) and any selfmap \(f : S \to S\) the Nielsen number \(N(f)\) equals the absolute value \(|L(f) |\) of the Lefschetz number.
Keppelmann, Edward C. +1 more
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SKT and tamed symplectic structures on solvmanifolds [PDF]
Tohoku Mathematical Journal, 2015 Final version of the paper "Tamed complex structures on solvmanifolds".
FINO, Anna Maria +2 more
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Small covers, infra-solvmanifolds and curvature [PDF]
Forum Mathematicum, 2014 Abstract It is shown that a small cover (resp. real moment-angle manifold) over a simple polytope is an infra-solvmanifold if and only if it is diffeomorphic to a real Bott manifold (resp. flat torus). Moreover, we obtain several equivalent conditions for a small cover to be homeomorphic to a real Bott manifold.
Kuroki, Shintarô +2 more
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Einstein solvmanifolds are standard [PDF]
Annals of Mathematics, 2010 We study Einstein manifolds admitting a transitive solvable Lie group of isometries (solvmanifolds). It is conjectured that these exhaust the class of noncompact homogeneous Einstein manifolds. J. Heber has showed that under certain simple algebraic condition called standard (i.e.
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Function theory on metabelian solvmanifold
Journal of Functional Analysis, 1972 AbstractThe Laplace operators for metabelian solvmanifolds are used to describe certain spaces of C∞ functions on metabelian solvmanifolds of interest in harmonic analysis.
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Periodic points on nilmanifolds and solvmanifolds [PDF]
Pacific Journal of Mathematics, 1994 Let \(M\) be a compact manifold and \(f:M \to M\) a self map on \(M\). For any natural number \(n\), the \(n\)-th iterate of \(f\) is the \(n\)-fold composition \(f^ n:M \to M\). The fixed point set of \(f\) is \(\text{fix} (f)=\{x \in M:f(x)=x\}\). We say that \(x \in M\) is a periodic point of \(f\) is \(x\) is a fixed point of some \(f^ n\) and we ...
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